Induced quantum numbers in a (2+1)-dimensional electron gas

A gas of electrons confined to a plane is examined in both the relativistic and nonrelativistic case. Using a (0+1)-dimensional effective theory, a remarkably simple method is proposed to calculate the spin density induced by a uniform magnetic background field. The physical properties of possible fluxon excitations are determined. It is found that while in the relativistic case they can be considered as half-fermions (semions) in that they carry half a fermion charge and half the spin of a fermion, in the nonrelativistic case they should be thought of as fermions, having the charge and spin of a fermion.